Interacting classical dimers on the square lattice

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions ...

We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, w...

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interactions that can be used to suppress the li...

We study phases and transitions of the square-lattice double dimer model, consisting of two coupled replicas of the classical dimer model. As on the cubic lattice, we find a thermal phase transition from the Coulomb phase, a disordered but correlated dimer liquid, to a phase where fluctuations of the two replicas are closely synchronized with one another. Surprisingly, and in contrast to the cubic case, the phase boundary includes the noninteracting point, as we establish usi...

We present a quantum Monte Carlo investigation of the finite-temperature phase diagram of the quantum dimer model on the square lattice. We use the sweeping cluster algorithm, which allows to implement exactly the dimer constraint, supplemented with a equal-time directed loop move that allows to sample winding sectors. We find a high-temperature critical phase with power-law correlations that extend down to the Rokshar-Kivelson point, in the vicinity of which a re-entrance ef...

We study a model of two-dimensional classical dimers on the square lattice with strong geometric constraints (there is exactly one bond with the nearest point for every point in the lattice). This model corresponds to the quantum dimer model suggested by D.S. Rokhsar and S.A. Kivelson (1988). We use the directed-loop algorithm to show the system undergoes a Berezinskii-Kostelitz Thousless transition (BKT transition) in finite temperatures. After that, if we destroy the geomet...

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to det...

Close-packed, classical dimer models on three-dimensional, bipartite lattices harbor a Coulomb phase with power-law correlations at infinite temperature. Here, we discuss the nature of the thermal phase transition out of this Coulomb phase for a variety of dimer models which energetically favor crystalline dimer states with columnar ordering. For a family of these models we find a direct thermal transition from the Coulomb phase to the dimer crystal. While some systems exhibi...

We present an extensive numerical study of the critical behavior of dimer models in three dimensions, focusing on the phase transition between Coulomb and crystalline columnar phases. The case of attractive interactions between parallel dimers on a plaquette was shown to undergo a continuous phase transition with critical exponents close to those of the O(N) tricritical universality class, a situation which is not easily captured by conventional field theories. That the dimer...

Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $\nu$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the lowtemperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer casewith finite chemical potential $\mu$, we also find an o...